Utilities often connect capacitor banks to electric power systems to reduce system losses and improve voltage regulation. Practical manufacturing limitations for individual capacitor units and typical capacitance and voltage requirements of power systems favor capacitor bank designs as a series/parallel matrix of capacitor units. The matrix includes multiple strings of in-series capacitor units connected in a parallel arrangement. The series connections of the capacitor units satisfy the voltage requirements; the parallel connections of the strings satisfy the capacitance requirements.
Oftentimes, capacitor banks are connected to electric power systems in phase-neutral—rather that in-series, or in-line—arrangements. Such arrangements are commonly referred to as “shunt” configurations. The capacitor bank may be grounded with a neutral point of the capacitor bank being connected to a power system ground via an intentionally low impedance tie.
A popular capacitor bank construction style is a “fuseless capacitor bank” design. This design includes a reduced physical size and cost relative to other traditional capacitor bank designs because it does not include any fuses for isolating failed capacitor units. Instead, the fuseless capacitor bank design exploits the failure mode of a capacitor, namely, a short circuit. If a capacitor unit within the capacitor bank fails, internal capacitor bank voltages will be altered, increasing across the remaining, functioning units within the effected string. If the number of units per string is large, the increased voltage due to a single unit failure is manageable. Eventually, however, the increased voltage may reach damaging thresholds if more units in the string fail. If this elevated voltage is not detected, and, when necessary, the entire capacitor bank is not de-energized in response, cascading and often catastrophic failures may result.
One way to determine whether potentially damaging voltage levels exist is to measure the voltage stress across each unit within the capacitor bank. However, this technique is impractical due to the large number of units present in a typical capacitor bank. Therefore, existing protection systems generally employ indirect measurements, measuring voltages external to the capacitor bank and possibly current flows through various branches in the capacitor bank, along with well-understood equations, to estimate internal voltage levels.
These measurements assume the application of impedance-based protection as the means to detect failure of capacitor units. The general Ohms law expression is V=I*Z, where the voltage (V) measured across any electrical component is equal to the current flow (I) through the component times the impedance (Z) of the component. Impedance for each string of the capacitor bank may be calculated based on measured line-ground voltage and string current values as follows:
Measured String Impedance=Zmeas,n=V÷In, where “n” represents the nth string. This measurement is repeated for each nth string, where n=1, 2, 3, . . . , n, . . . , CNT. CNT is a total count of the strings (per phase). Although illustrated in FIG. 2 as having six strings per phase, a person having ordinary skill in the art and having the benefit of the present disclosure will recognize that any number of strings per phase may be utilized. A response characteristic of a protective device associated with the capacitor bank may be plotted on a complex impedance plane, with capacitive resistance (R) plotted on the x axis and capacitive reactance (jX) plotted on the y axis.
FIG. 1 illustrates a traditional complex impedance plane 100 for a capacitor string. Znom represents the nominal impedance of the string. This value is entirely capacitive reactance, as seen by the −jX placement on the impedance plane 100. An operator can calculate Znom from nameplate data of the capacitor units in the capacitor bank. Initially, Znom equals a value in the center of a plotted circle, Zcenter. During energized operation of a capacitor bank with no failed units (a “healthy bank”), the measured impedance should be nearly equal to the center: Zmeas,n=Zcenter. If the capacitor bank includes failed units, Zmeas,n will move from the center of the circle, towards an outer edge of the circle. If Zmeas,n passes the outer edge of the circle, a system failure is detected. Detection sensitivity may be adjusted by altering the radius of the circle. A small radius corresponds to higher sensitivity than a large radius.
Typically, polyethylene film separates internal aluminum foil plates of each capacitor. The polyethylene film expands and contracts with temperature. This temperature dependence results in changes in capacitance and, therefore, capacitor bank impedance. As temperature goes up, impedance goes up and capacitance goes down. The net capacitor bank impedance change caused by a temperature fluctuation can cause Zmeas,n to move outside the circle, resulting in detection of a system failure. Such a detection is a “false alarm” because it resulted from a temperature fluctuation and not a system failure.
Conventional approaches to preventing these false alarms include expanding the size of the circle in the impedance plane 100. If the circle is expanded enough, temperature-induced impedance changes will not result in failure detection. This approach does not discriminate between impedance changes due to temperature and those due to capacitor unit failures. Rather, it de-sensitizes overall protection, preventing false alarms caused by temperature changes but also reducing the ability to detect bona fide unit failures. Thus, unit failures resulting in minor impedance changes may not be detected.
Another conventional approach is to directly measure ambient temperature using a temperature transducer mounted externally to the capacitor bank. The size and location of the circle in the impedance plane 100 is adjusted based on the measured temperature, in accordance with a theoretical rate of impedance change per temperature variant. The drawbacks of this approach include the high cost and low reliability of adding the temperature transducer components to the system. Another drawback is that this approach does not account for possible discrepancies between the temperature at the transducer location and the temperatures within the capacitor bank. Partial shading of various portions of the bank may lead to non-homogenous capacitor temperatures and the inability to properly calculate impedance changes.
Therefore, a need exists in the art for a system and method for protecting an electric device using temperature compensation. In particular, a need exists in the art for a system and method for compensating for temperature-induced capacitance variations in a capacitor bank.